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\"cnl.h\"\n#include \n\ntemplate\nusing fp = cnl::fixed_point, -n>;\n\nint main() {\n constexpr auto n = 8;\n using fp_n = fp;\n using integer = typename fp_n::rep;\n std::printf(\"n=%d\\n\", n);\n std::printf(\"digits=%d\\n\", (int)cnl::digits_v);\n std::printf(\"integer range=[%ld..%ld]\\n\", (long)cnl::numeric_limits::min(), (long)cnl::numeric_limits::max());\n std::printf(\"scale=1/%ld = %.20Lf\\n\", 1L<()(1));\n std::printf(\"range=[%.20Lf..%.20Lf]\\n\", (long double)cnl::numeric_limits::min(), (long double)cnl::numeric_limits::max());\n}\n","codes",[3388],{"_3389":3390,"_3384":3391},"file","cnl.h","\n// Copyright John McFarlane 2018.\n// Distributed under the Boost Software License, Version 1.0.\n// (See accompanying file ../LICENSE_1_0.txt or copy at\n// http://www.boost.org/LICENSE_1_0.txt)\n\n// mechanically retrieved, single-header version of CNL library\n// https://github.com/johnmcfarlane/cnl\n\n#if ! defined(CNL_COMPLETE_H)\n#define CNL_COMPLETE_H\n\n#if (__cplusplus < 201703L)\n#error This build of CNL requires C++17 or above.\n#endif\n\n#include \n#include \n#include \n#include \n#include \n#include \n#include \n#include \n\nnamespace cnl {\n namespace _impl {\n template\n constexpr T max(T a, T b)\n {\n return (a\n constexpr T min(T a, T b)\n {\n return (a\n constexpr T deleted_fn() = delete;\n }\n}\nnamespace cnl {\n using int8 = std::int8_t;\n using uint8 = std::uint8_t;\n using int16 = std::int16_t;\n using uint16 = std::uint16_t;\n using int32 = std::int32_t;\n using uint32 = std::uint32_t;\n using int64 = std::int64_t;\n using uint64 = std::uint64_t;\n using int128 = __int128;\n using uint128 = unsigned __int128;\n using intmax = int128;\n using uintmax = uint128;\n namespace _cnlint_impl {\n template\n constexpr intmax parse(char const* s, int base, ParseDigit parse_digit, intmax value = 0)\n {\n return (*s) ? parse(s+1, base, parse_digit, parse_digit(*s)+value*base) : value;\n }\n constexpr int parse_bin_char(char c) {\n return (c == '0') ? 0 : (c == '1') ? 1 : int{};\n }\n constexpr int parse_dec_char(char c) {\n return (c >= '0' && c <= '9') ? c - '0' : int{};\n }\n constexpr int parse_oct_char(char c) {\n return (c >= '0' && c <= '7') ? c - '0' : int{};\n }\n constexpr int parse_hex_char(char c) {\n return (c >= '0' && c <= '9')\n ? c - '0'\n : (c >= 'a' && c <= 'z')\n ? c + 10 - 'a'\n : (c >= 'A' && c <= 'Z')\n ? c + 10 - 'A'\n : int{};\n }\n template\n constexpr intmax parse(const char (& s)[NumChars])\n {\n return (s[0]!='0')\n ? parse(s, 10, parse_dec_char)\n : (s[1]=='x' || s[1]=='X')\n ? parse(s+2, 16, parse_hex_char)\n : (s[1]=='b' || s[1]=='B')\n ? parse(s+2, 2, parse_bin_char)\n : parse(s+1, 8, parse_oct_char);\n }\n template\n constexpr intmax parse() {\n return parse({Chars...,'\\0'});\n }\n }\n}\n \nnamespace cnl {\n template\n struct numeric_limits : std::numeric_limits {};\n template<>\n struct numeric_limits : numeric_limits {\n static int const digits = 8*sizeof(int128)-1;\n static int const digits10 = 38;\n struct _s {\n constexpr _s(uint64 upper, uint64 lower) : value(lower + (int128{upper} << 64)) {}\n constexpr operator int128() const { return value; }\n int128 value;\n };\n static constexpr int128 min()\n {\n return _s(0x8000000000000000, 0x0000000000000000);\n }\n static constexpr int128 max()\n {\n return _s(0x7fffffffffffffff, 0xffffffffffffffff);\n }\n static constexpr int128 lowest()\n {\n return min();\n }\n };\n template<>\n struct numeric_limits : numeric_limits {\n static int const digits = 8*sizeof(int128);\n static int const digits10 = 38;\n struct _s {\n constexpr _s(uint64 upper, uint64 lower) : value(lower + (uint128{upper} << 64)) {}\n constexpr operator uint128() const { return value; }\n uint128 value;\n };\n static constexpr int128 min()\n {\n return 0;\n }\n static constexpr uint128 max()\n {\n return _s(0xffffffffffffffff, 0xffffffffffffffff);\n }\n static constexpr int128 lowest()\n {\n return min();\n }\n };\n}\nnamespace cnl {\n template< ::cnl::intmax Value>\n struct constant {\n using value_type = decltype(Value);\n static constexpr value_type value = Value;\n constexpr operator value_type() const {\n return value;\n }\n };\n template< ::cnl::intmax Value> constexpr auto operator +(constant) noexcept -> constant<+ Value> { return constant<+ Value>{}; }\n template< ::cnl::intmax Value> constexpr auto operator -(constant) noexcept -> constant<- Value> { return constant<- Value>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator +(constant, constant) noexcept -> constant<(LhsValue + RhsValue)> { return constant<(LhsValue + RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator -(constant, constant) noexcept -> constant<(LhsValue - RhsValue)> { return constant<(LhsValue - RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator *(constant, constant) noexcept -> constant<(LhsValue * RhsValue)> { return constant<(LhsValue * RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator /(constant, constant) noexcept -> constant<(LhsValue / RhsValue)> { return constant<(LhsValue / RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator %(constant, constant) noexcept -> constant<(LhsValue % RhsValue)> { return constant<(LhsValue % RhsValue)>{}; }\n template< ::cnl::intmax Value> constexpr auto operator ~(constant) noexcept -> constant<~ Value> { return constant<~ Value>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator &(constant, constant) noexcept -> constant<(LhsValue & RhsValue)> { return constant<(LhsValue & RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator |(constant, constant) noexcept -> constant<(LhsValue | RhsValue)> { return constant<(LhsValue | RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator ^(constant, constant) noexcept -> constant<(LhsValue ^ RhsValue)> { return constant<(LhsValue ^ RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator <<(constant, constant) noexcept -> constant<(LhsValue << RhsValue)> { return constant<(LhsValue << RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator >>(constant, constant) noexcept -> constant<(LhsValue >> RhsValue)> { return constant<(LhsValue >> RhsValue)>{}; }\n template< ::cnl::intmax Value> constexpr auto operator !(constant) noexcept -> constant { return constant{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator &&(constant, constant) noexcept -> constant<(LhsValue && RhsValue)> { return constant<(LhsValue && RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator ||(constant, constant) noexcept -> constant<(LhsValue || RhsValue)> { return constant<(LhsValue || RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator ==(constant, constant) noexcept -> constant<(LhsValue == RhsValue)> { return constant<(LhsValue == RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator !=(constant, constant) noexcept -> constant<(LhsValue != RhsValue)> { return constant<(LhsValue != RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator <(constant, constant) noexcept -> constant<(LhsValue < RhsValue)> { return constant<(LhsValue < RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator >(constant, constant) noexcept -> constant<(LhsValue > RhsValue)> { return constant<(LhsValue > RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator <=(constant, constant) noexcept -> constant<(LhsValue <= RhsValue)> { return constant<(LhsValue <= RhsValue)>{}; }\n template< ::cnl::intmax LhsValue, ::cnl::intmax RhsValue> constexpr auto operator >=(constant, constant) noexcept -> constant<(LhsValue >= RhsValue)> { return constant<(LhsValue >= RhsValue)>{}; }\n namespace _impl {\n template\n struct is_constant : std::false_type {\n };\n template< ::cnl::intmax Value>\n struct is_constant<::cnl::constant> : std::true_type {\n };\n }\n namespace literals {\n template\n constexpr auto operator \"\" _c()\n -> constant<_cnlint_impl::parse()>\n {\n return {};\n }\n }\n template< ::cnl::intmax Value>\n struct numeric_limits> : cnl::numeric_limits::value_type> {\n using _value_type = typename constant::value_type;\n static constexpr _value_type min()\n {\n return {};\n }\n static constexpr _value_type max()\n {\n return {};\n }\n static constexpr _value_type lowest()\n {\n return {};\n }\n };\n}\nnamespace cnl {\n namespace _impl {\n template\n using common_type_t = typename std::common_type::type;\n template\n using enable_if_t = typename std::enable_if::type;\n template\n constexpr bool identical(A const& a, B const& b)\n {\n static_assert(std::is_same::value, \"different types\");\n return a==b;\n }\n }\n}\nnamespace cnl {\n using _digits_type = int;\n template\n struct is_composite : std::false_type {\n static_assert(!std::is_reference::value, \"T is a reference\");\n static_assert(!std::is_const::value, \"T is const\");\n static_assert(!std::is_volatile::value, \"T is volatile\");\n };\n template\n constexpr auto is_composite_v = is_composite::value;\n namespace _num_traits_impl {\n template\n struct are_composite;\n template<>\n struct are_composite<> : std::false_type {\n };\n template\n struct are_composite\n : std::integral_constant::type>::value || are_composite::value> {\n };\n template<_digits_type MinNumDigits, class Smaller, class T>\n struct enable_for_range\n : std::enable_if::digits &&\n numeric_limits::digits < MinNumDigits> {\n };\n template<_digits_type MinNumDigits, class Smallest>\n struct enable_for_range\n : std::enable_if::digits> {\n };\n template<_digits_type MinNumDigits, class Smaller, class T>\n using enable_for_range_t = typename enable_for_range::type;\n template<_digits_type MinNumDigits, class Enable = void>\n struct set_digits_signed;\n template<_digits_type MinNumDigits>\n struct set_digits_signed> {\n using type = int8;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_signed> {\n using type = int16;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_signed> {\n using type = int32;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_signed> {\n using type = int64;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_signed> {\n using type = int128;\n };\n template<_digits_type MinNumDigits, class Enable = void>\n struct set_digits_unsigned;\n template<_digits_type MinNumDigits>\n struct set_digits_unsigned> {\n using type = uint8;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_unsigned> {\n using type = uint16;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_unsigned> {\n using type = uint32;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_unsigned> {\n using type = uint64;\n };\n template<_digits_type MinNumDigits>\n struct set_digits_unsigned> {\n using type = uint128;\n };\n template\n using set_digits_integer = typename std::conditional<\n numeric_limits::is_signed,\n set_digits_signed,\n set_digits_unsigned>::type;\n }\n template\n struct digits : std::integral_constant<_digits_type, numeric_limits::digits> {\n static_assert(numeric_limits::is_specialized, \"cnl::digits is not correctly specialized for T\");\n };\n template\n constexpr _digits_type digits_v = digits::value;\n template\n struct set_digits;\n template\n struct set_digits::value>>\n : _num_traits_impl::set_digits_integer {\n };\n template<_digits_type Digits>\n struct set_digits\n : _num_traits_impl::set_digits_integer {\n };\n template<_digits_type Digits>\n struct set_digits\n : _num_traits_impl::set_digits_integer {\n };\n template\n using set_digits_t = typename set_digits::type;\n template\n struct is_integral : std::is_integral {\n };\n template<>\n struct is_integral : std::integral_constant {\n };\n template<>\n struct is_integral : std::integral_constant {\n };\n template\n struct is_signed : std::integral_constant::is_signed> {\n };\n template\n struct make_signed;\n template\n struct make_signed::value>> : std::make_signed {\n };\n template\n using make_signed_t = typename make_signed::type;\n template\n struct make_unsigned;\n template\n struct make_unsigned::value>> : std::make_unsigned {\n };\n template<>\n struct make_unsigned {\n using type = uint128;\n };\n template<>\n struct make_unsigned {\n using type = uint128;\n };\n template<>\n struct make_signed {\n using type = int128;\n };\n template<>\n struct make_signed {\n using type = int128;\n };\n template\n using make_unsigned_t = typename make_unsigned::type;\n namespace _impl {\n template\n struct make_signed;\n template\n struct make_signed : ::cnl::make_signed {\n };\n template\n struct make_signed : ::cnl::make_unsigned {\n };\n template\n using make_signed_t = typename make_signed::type;\n template\n struct common_signedness {\n static constexpr bool _are_signed = numeric_limits::is_signed | numeric_limits::is_signed;\n using type = typename std::common_type,\n make_signed_t>::type;\n };\n template\n using common_signedness_t = typename common_signedness::type;\n template\n struct is_integer_or_float : std::integral_constant<\n bool,\n numeric_limits::is_integer || numeric_limits::is_iec559> {\n };\n }\n template\n constexpr Number to_rep(Number const& number) {\n return number;\n }\n namespace _impl {\n using cnl::to_rep;\n template\n using to_rep_t = decltype(to_rep(std::declval()));\n }\n template\n struct from_rep;\n template\n struct from_rep::value>> {\n template\n constexpr Number operator()(Rep const& rep) const {\n return static_cast(rep);\n }\n };\n namespace _impl {\n template::value, int> dummy = 0>\n constexpr Result for_rep(F f, Args &&...args) {\n return f(std::forward(args)...);\n }\n template::value, int> dummy = 0>\n constexpr Result for_rep(F f, Args &&...args) {\n return for_rep(f, to_rep(std::forward(args))...);\n }\n }\n namespace _num_traits_impl {\n template\n struct make_integer;\n template\n struct make_integer {\n using type = set_digits_t;\n };\n template\n struct make_integer {\n using type = set_digits_t;\n };\n template\n using make_integer_t = typename make_integer::type;\n }\n template\n struct from_value {\n using type = void;\n };\n template\n struct from_value::value>> {\n using type = typename std::conditional<\n cnl::is_integral::value,\n Value,\n _num_traits_impl::make_integer_t::value, cnl::is_signed::value>>::type;\n };\n template\n using from_value_t = typename from_value::type;\n namespace _impl {\n template\n constexpr auto from_value(Value const& value)\n -> cnl::from_value_t\n {\n static_assert(\n !std::is_same>::value,\n \"cnl::from_value is missing a specialization\");\n return value;\n }\n }\n template< ::cnl::intmax ConstantValue, class InputValue>\n struct from_value, InputValue> {\n using type = constant;\n };\n template\n struct shift;\n namespace _impl {\n template\n struct default_shift;\n template\n struct default_shift> {\n constexpr auto operator()(S const& s) const\n -> decltype(s*(S{1} << constant{}))\n {\n return s*(S{1} << constant{});\n }\n };\n template\n struct default_shift> {\n constexpr auto operator()(S const& s) const\n -> decltype(s/(S{1} << constant<-Bits>()))\n {\n return s/(S{1} << constant<-Bits>());\n }\n };\n }\n template\n struct shift::value>>\n : _impl::default_shift {\n };\n namespace _impl {\n template\n constexpr auto shift(S const& s)\n -> decltype(cnl::shift{}(s))\n {\n return cnl::shift{}(s);\n }\n }\n template\n struct scale {\n constexpr S operator()(S const& s) const\n {\n return static_cast(shift()(s));\n }\n };\n namespace _impl {\n template\n constexpr S scale(S const& s)\n {\n return cnl::scale()(s);\n }\n }\n}\nnamespace cnl {\n namespace _bit_impl {\n template\n constexpr bool is_integral_unsigned()\n {\n return numeric_limits::is_integer && !is_signed::value;\n }\n template\n constexpr bool is_integral_signed()\n {\n return numeric_limits::is_integer && is_signed::value;\n }\n template\n constexpr T rotl(T x, unsigned int s, unsigned int width) noexcept\n {\n static_assert(is_integral_unsigned(), \"T must be unsigned integer\");\n return s%width==0 ? x : static_cast((x << (s%width)) | (x >> (width-(s%width))));\n }\n template\n constexpr T rotr(T x, unsigned int s, unsigned int width) noexcept\n {\n static_assert(is_integral_unsigned(), \"T must be unsigned integer\");\n return s%width==0 ? x : static_cast((x >> (s%width)) | (x << (width-(s%width))));\n }\n template\n constexpr int countr_zero(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return (x & 1) ? 0 : countr_zero(static_cast(x >> 1))+1;\n }\n }\n template\n constexpr T rotl(T x, unsigned int s) noexcept\n {\n return _bit_impl::rotl(x, s, cnl::digits::value);\n }\n template\n constexpr T rotr(T x, unsigned int s) noexcept\n {\n return _bit_impl::rotr(x, s, cnl::digits::value);\n }\n template\n constexpr int countl_zero(T x) noexcept;\n template<>\n constexpr int countl_zero(unsigned int x) noexcept\n {\n return x ? __builtin_clz(x) : cnl::digits::value;\n }\n template<>\n constexpr int countl_zero(unsigned long x) noexcept\n {\n return x ? __builtin_clzl(x) : cnl::digits::value;\n }\n template<>\n constexpr int countl_zero(unsigned long long x) noexcept\n {\n return x ? __builtin_clzll(x) : cnl::digits::value;\n }\n template\n constexpr int countl_zero(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return x ? countl_zero(static_cast(x >> 1))-1 : cnl::digits::value;\n }\n template\n constexpr int countl_one(T x) noexcept;\n template<>\n constexpr int countl_one(unsigned int x) noexcept\n {\n return ~x ? __builtin_clz(~x) : cnl::digits::value;\n }\n template<>\n constexpr int countl_one(unsigned long x) noexcept\n {\n return ~x ? __builtin_clzl(~x) : cnl::digits::value;\n }\n template<>\n constexpr int countl_one(unsigned long long x) noexcept\n {\n return ~x ? __builtin_clzll(~x) : cnl::digits::value;\n }\n template\n constexpr int countl_one(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return (x & (T{1} << (cnl::digits::value-1))) ? countl_one(static_cast(x << 1))+1 : 0;\n }\n template\n constexpr int countr_zero(T x) noexcept;\n template<>\n constexpr int countr_zero(unsigned int x) noexcept\n {\n return __builtin_ctz(x);\n }\n template<>\n constexpr int countr_zero(unsigned long x) noexcept\n {\n return x ? __builtin_ctzl(x) : cnl::digits::value;\n }\n template<>\n constexpr int countr_zero(unsigned long long x) noexcept\n {\n return x ? __builtin_ctzll(x) : cnl::digits::value;\n }\n template\n constexpr int countr_zero(T x) noexcept\n {\n return x ? _bit_impl::countr_zero(x) : cnl::digits::value;\n }\n template\n constexpr int countr_one(T x) noexcept;\n template<>\n constexpr int countr_one(unsigned int x) noexcept\n {\n return countr_zero(~x);\n }\n template\n constexpr int countr_one(T x) noexcept\n {\n return (x & T{1}) ? countr_one(x >> 1)+1 : 0;\n }\n template\n constexpr int popcount(T x) noexcept;\n template<>\n constexpr int popcount(unsigned int x) noexcept\n {\n return __builtin_popcount(x);\n }\n template<>\n constexpr int popcount(unsigned long x) noexcept\n {\n return __builtin_popcountl(x);\n }\n template<>\n constexpr int popcount(unsigned long long x) noexcept\n {\n return __builtin_popcountll(x);\n }\n template\n constexpr int popcount(T x) noexcept\n {\n return x ? popcount(x & (x-1))+1 : 0;\n }\n template\n constexpr bool ispow2(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return x && !(x & (x-1));\n }\n template\n constexpr T ceil2(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return x ? static_cast(T{1} << (digits::value-countl_zero(T(x-T(1))))) : T{0};\n }\n template\n constexpr T floor2(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return x ? static_cast(T{1} << (digits::value-1-countl_zero(x))) : T{0};\n }\n template\n constexpr int log2p1(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return digits::value-countl_zero(x);\n }\n template\n constexpr int countl_rsb(T x) noexcept;\n template<>\n constexpr int countl_rsb(int x) noexcept\n {\n return __builtin_clrsb(x);\n }\n template<>\n constexpr int countl_rsb(long x) noexcept\n {\n return __builtin_clrsbl(x);\n }\n template<>\n constexpr int countl_rsb(long long x) noexcept\n {\n return __builtin_clrsbll(x);\n }\n template\n constexpr int countl_rsb(T x) noexcept\n {\n static_assert(_bit_impl::is_integral_signed(), \"T must be signed integer\");\n using unsigned_type = typename make_unsigned::type;\n return ((x<0)\n ? countl_one(static_cast(x))\n : countl_zero(static_cast(x))) - 1;\n }\n namespace _bit_impl {\n template\n struct countl_rb {\n template\n constexpr int operator()(Integer const& value) const\n {\n static_assert(_bit_impl::is_integral_unsigned(), \"T must be unsigned integer\");\n return countl_zero(value);\n }\n };\n template<>\n struct countl_rb {\n template\n constexpr int operator()(Integer const& value) const\n {\n static_assert(_bit_impl::is_integral_signed(), \"T must be signed integer\");\n return countl_rsb(value);\n }\n };\n }\n template\n constexpr int countl_rb(T x) noexcept\n {\n return _bit_impl::countl_rb::value>()(x);\n }\n template\n constexpr int countr_used(T x) noexcept\n {\n return digits::value - countl_rb(x);\n }\n}\n \nnamespace cnl {\n template\n constexpr T sqrt(T arg) {\n return std::sqrt(arg);\n }\n}\nnamespace cnl {\n namespace math_constants {\n template inline constexpr T e{_impl::deleted_fn()};\n template inline constexpr T log2e{_impl::deleted_fn()};\n template inline constexpr T log10e{_impl::deleted_fn()};\n template inline constexpr T pi{_impl::deleted_fn()};\n template inline constexpr T invpi{_impl::deleted_fn()};\n template inline constexpr T invsqrtpi{_impl::deleted_fn()};\n template inline constexpr T ln2{_impl::deleted_fn()};\n template inline constexpr T ln10{_impl::deleted_fn()};\n template inline constexpr T sqrt2{_impl::deleted_fn()};\n template inline constexpr T sqrt3{_impl::deleted_fn()};\n template inline constexpr T invsqrt2{sqrt2/2};\n template inline constexpr T invsqrt3{_impl::deleted_fn()};\n template inline constexpr T radian{_impl::deleted_fn()};\n template inline constexpr T egamma{_impl::deleted_fn()};\n template inline constexpr T phi{_impl::deleted_fn()};\n template inline constexpr T catalan{_impl::deleted_fn()};\n template inline constexpr T apery{_impl::deleted_fn()};\n template inline constexpr T glaisher{_impl::deleted_fn()};\n template<> inline constexpr long double e{2.718281828459045235360287471352662498L};\n template<> inline constexpr long double log2e{1.442695040888963407359924681001892137L};\n template<> inline constexpr long double log10e{0.434294481903251827651128918916605082L};\n template<> inline constexpr long double pi{3.141592653589793238462643383279502884L};\n template<> inline constexpr long double invpi{0.318309886183790671537767526745028724L};\n template<> inline constexpr long double invsqrtpi{\n 0.564189583547756286948079451560772585844050629329L};\n template<> inline constexpr long double ln2{0.693147180559945309417232121458176568L};\n template<> inline constexpr long double ln10{2.302585092994045684017991454684364208L};\n template<> inline constexpr long double sqrt2{1.414213562373095048801688724209698079L};\n template<> inline constexpr long double sqrt3{\n 1.73205080756887729352744634150587236694280525381038062805580L};\n template<> inline constexpr long double invsqrt3{\n 0.57735026918962576450914878050195745564760175127013L};\n template<> inline constexpr long double radian{\n 57.295779513082320876798154814105170332405472466564L};\n template<> inline constexpr long double egamma{0.5772156649015328606065120900824024L};\n template<> inline constexpr long double phi{1.6180339887498948482045868343656381L};\n template<> inline constexpr long double catalan{0.915965594177219015054603514932384110774L};\n template<> inline constexpr long double apery{1.202056903159594285399738161511449990L};\n template<> inline constexpr long double glaisher{1.282427129100622636875342568869791727L};\n template<> inline constexpr double e{2.7182818284590452354};\n template<> inline constexpr double log2e{1.4426950408889634074};\n template<> inline constexpr double log10e{0.43429448190325182765};\n template<> inline constexpr double pi{3.14159265358979323846};\n template<> inline constexpr double invpi{0.31830988618379067154};\n template<> inline constexpr double invsqrtpi{0.564189583547756286948079451560772585844050629329};\n template<> inline constexpr double ln2{0.69314718055994530942};\n template<> inline constexpr double ln10{2.30258509299404568402};\n template<> inline constexpr double sqrt2{1.41421356237309504880};\n template<> inline constexpr double sqrt3{\n 1.73205080756887729352744634150587236694280525381038062805580};\n template<> inline constexpr double invsqrt3{0.57735026918962576450914878050195745564760175127013};\n template<> inline constexpr double radian{57.295779513082320876798154814105170332405472466564};\n template<> inline constexpr double egamma{0.5772156649015328606065120900824024};\n template<> inline constexpr double phi{1.6180339887498948482045868343656381};\n template<> inline constexpr double catalan{0.915965594177219015054603514932384110774};\n template<> inline constexpr double apery{1.202056903159594285399738161511449990};\n template<> inline constexpr double glaisher{1.282427129100622636875342568869791727};\n template<> inline constexpr float e{2.7182818284590452354f};\n template<> inline constexpr float log2e{1.4426950408889634074f};\n template<> inline constexpr float log10e{0.43429448190325182765f};\n template<> inline constexpr float pi{3.14159265358979323846f};\n template<> inline constexpr float invpi{0.31830988618379067154f};\n template<> inline constexpr float invsqrtpi{0.564189583547756286948079451560772585844050629329f};\n template<> inline constexpr float ln2{0.69314718055994530942f};\n template<> inline constexpr float ln10{2.30258509299404568402f};\n template<> inline constexpr float sqrt2{1.41421356237309504880f};\n template<> inline constexpr float sqrt3{1.73205080756887729352744634150587236694280525381038062805580f};\n template<> inline constexpr float invsqrt3{0.57735026918962576450914878050195745564760175127013f};\n template<> inline constexpr float radian{57.295779513082320876798154814105170332405472466564f};\n template<> inline constexpr float egamma{0.5772156649015328606065120900824024f};\n template<> inline constexpr float phi{1.6180339887498948482045868343656381f};\n template<> inline constexpr float catalan{0.915965594177219015054603514932384110774f};\n template<> inline constexpr float apery{1.202056903159594285399738161511449990f};\n template<> inline constexpr float glaisher{1.282427129100622636875342568869791727f};\n }\n namespace _numeric_impl {\n template\n struct trailing_bits {\n constexpr int operator()(Integer const& integer) const noexcept\n {\n return countr_zero(integer);\n }\n };\n template\n struct trailing_bits {\n constexpr int operator()(Integer const& integer) const noexcept\n {\n using unsigned_type = make_unsigned_t;\n return countr_zero(static_cast(integer));\n }\n };\n }\n template\n constexpr int trailing_bits(Integer const& value)\n {\n return value ? _numeric_impl::trailing_bits::value>()(value) : 0;\n }\n namespace _numeric_impl {\n template\n constexpr int used_bits_positive(Integer const& value, int mask_bits = cnl::digits::value/2)\n {\n static_assert(cnl::numeric_limits::is_integer,\n \"Integer parameter of used_bits_positive() must be a fundamental integer.\");\n return (value>=(Integer{1} << mask_bits))\n ? mask_bits+used_bits_positive(value/(Integer{1} << mask_bits), mask_bits)\n : (mask_bits>1)\n ? used_bits_positive(value, mask_bits/2)\n : 1;\n }\n }\n namespace _numeric_impl {\n template\n struct used_bits {\n template\n constexpr int operator()(Integer const& value) const\n {\n return value ? used_bits_positive(value) : 0;\n }\n };\n template<>\n struct used_bits {\n template\n constexpr int operator()(Integer const& value) const\n {\n static_assert(cnl::numeric_limits::is_integer,\n \"Integer parameter of used_bits()() must be a fundamental integer.\");\n return (value>0)\n ? used_bits_positive(value)\n : (value==0)\n ? 0\n : used_bits()(Integer(-1)-value);\n }\n };\n }\n template\n constexpr int used_bits(Integer const& value)\n {\n return _impl::for_rep(_numeric_impl::used_bits::value>(), value);\n }\n template\n constexpr int leading_bits(Integer const& value)\n {\n return digits::value-used_bits(value);\n }\n}\nnamespace cnl {\n namespace _impl {\n template\n struct wants_generic_ops : std::false_type {\n };\n struct binary_op {\n using is_not_comparison = void;\n };\n struct comparison_op {\n using is_comparison = void;\n };\n struct minus_op {\n template\n constexpr auto operator()(Rhs const& rhs) const -> decltype(-rhs)\n {\n return -rhs;\n }\n };\n struct plus_op {\n template\n constexpr auto operator()(Rhs const& rhs) const -> decltype(+rhs)\n {\n return +rhs;\n }\n };\n struct add_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs+rhs)\n {\n return lhs+rhs;\n }\n };\n struct subtract_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs-rhs)\n {\n return lhs-rhs;\n }\n };\n struct multiply_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs*rhs)\n {\n return lhs*rhs;\n }\n };\n struct divide_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs/rhs)\n {\n return lhs/rhs;\n }\n };\n struct modulo_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs%rhs)\n {\n return lhs%rhs;\n }\n };\n struct bitwise_or_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs | rhs)\n {\n return lhs | rhs;\n }\n };\n struct bitwise_and_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs & rhs)\n {\n return lhs & rhs;\n }\n };\n struct bitwise_xor_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs ^ rhs)\n {\n return lhs ^ rhs;\n }\n };\n struct shift_left_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs << rhs)\n {\n return lhs << rhs;\n }\n };\n struct shift_right_op : binary_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs >> rhs)\n {\n return lhs >> rhs;\n }\n };\n struct equal_op : comparison_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs==rhs)\n {\n return lhs==rhs;\n }\n };\n struct not_equal_op : comparison_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs!=rhs)\n {\n return lhs!=rhs;\n }\n };\n struct less_than_op : comparison_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs>rhs)\n {\n return lhs>rhs;\n }\n };\n struct less_than_or_equal_op : comparison_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs<=rhs)\n {\n return lhs<=rhs;\n }\n };\n struct greater_than_or_equal_op : comparison_op {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const -> decltype(lhs>=rhs)\n {\n return lhs>=rhs;\n }\n };\n struct assign_add_op {\n using binary = add_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs += rhs)\n {\n return lhs += rhs;\n }\n };\n struct assign_subtract_op {\n using binary = subtract_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs -= rhs)\n {\n return lhs -= rhs;\n }\n };\n struct assign_multiply_op {\n using binary = multiply_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs *= rhs)\n {\n return lhs *= rhs;\n }\n };\n struct assign_divide_op {\n using binary = divide_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs /= rhs)\n {\n return lhs /= rhs;\n }\n };\n struct assign_modulo_op {\n using binary = modulo_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs %= rhs)\n {\n return lhs %= rhs;\n }\n };\n struct assign_bitwise_or_op {\n using binary = bitwise_or_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs |= rhs)\n {\n return lhs |= rhs;\n }\n };\n struct assign_bitwise_and_op {\n using binary = bitwise_and_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs &= rhs)\n {\n return lhs &= rhs;\n }\n };\n struct assign_bitwise_xor_op {\n using binary = bitwise_xor_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs ^= rhs)\n {\n return lhs ^= rhs;\n }\n };\n struct assign_shift_left_op {\n using binary = shift_left_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs <<= rhs)\n {\n return lhs <<= rhs;\n }\n };\n struct assign_shift_right_op {\n using binary = shift_right_op;\n template\n constexpr auto operator()(Lhs& lhs, Rhs const& rhs) const -> decltype(lhs >>= rhs)\n {\n return lhs >>= rhs;\n }\n };\n template\n using op_result = decltype(Operator()(std::declval(), std::declval()));\n template\n struct unary_operator;\n template\n struct binary_operator;\n template\n struct compound_assignment_operator {\n constexpr LhsOperand& operator()(LhsOperand& lhs, RhsOperand const& rhs) const\n {\n return lhs = static_cast(\n binary_operator()(lhs, rhs));\n }\n };\n }\n namespace _operators_impl {\n template\n using enable_unary_t = ::cnl::_impl::enable_if_t<_impl::wants_generic_ops::value, T>;\n template\n struct enable_binary;\n template\n struct enable_binary : std::false_type {\n };\n template\n struct enable_binary : std::false_type {\n };\n template\n struct enable_binary\n : std::integral_constant<\n bool,\n (numeric_limits::is_specialized && numeric_limits::is_specialized)\n && (_impl::wants_generic_ops::value\n || _impl::wants_generic_ops::value)> {\n };\n template\n using enable_binary_t = _impl::enable_if_t::value, T>;\n }\n template constexpr auto operator + (Operand const& operand) -> decltype(cnl::_impl::unary_operator, Operand>()(operand)) { return cnl::_impl::unary_operator()(operand); }\n template constexpr auto operator - (Operand const& operand) -> decltype(cnl::_impl::unary_operator, Operand>()(operand)) { return cnl::_impl::unary_operator()(operand); }\n template constexpr auto operator + (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator - (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator * (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator / (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator % (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator | (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator & (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator ^ (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator << (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator >> (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator == (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator != (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator < (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator > (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator <= (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator >= (LhsOperand const& lhs, RhsOperand const& rhs) -> decltype(cnl::_impl::binary_operator, LhsOperand, RhsOperand>()(lhs, rhs)) { return cnl::_impl::binary_operator()(lhs, rhs); }\n template constexpr auto operator += (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator -= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator *= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator /= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator %= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator |= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator &= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator ^= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator <<= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n template constexpr auto operator >>= (LhsOperand& lhs, RhsOperand const& rhs) -> cnl::_operators_impl::enable_binary_t()(lhs, rhs))> { return cnl::_impl::compound_assignment_operator()(lhs, rhs); }\n}\nnamespace cnl {\n namespace _impl {\n template\n class number_base;\n template\n constexpr Rep to_rep(number_base const& number);\n template\n class number_base {\n public:\n using rep = Rep;\n explicit constexpr operator bool() const\n {\n return static_cast(_rep);\n }\n protected:\n static_assert(numeric_limits::is_integer, \"number_base must be specialized with integer Rep type template parameter\");\n number_base() = default;\n explicit constexpr number_base(rep const& r)\n : _rep(r) { }\n template\n constexpr number_base& operator=(T const& r) {\n _rep = r;\n return static_cast(*this);\n }\n friend constexpr rep to_rep<>(number_base const&);\n private:\n rep _rep;\n };\n template\n struct is_class_derived_from_number_base : std::false_type {};\n template\n struct is_class_derived_from_number_base : is_class_derived_from_number_base {};\n template\n struct is_class_derived_from_number_base<\n Derived,\n enable_if_t, Derived>::value>>\n : std::true_type {};\n template\n struct is_derived_from_number_base : std::false_type {};\n template\n struct is_derived_from_number_base::value>>\n : is_class_derived_from_number_base { };\n template()))>\n struct depth;\n template\n struct depth {\n static constexpr auto value = depth::value + 1;\n };\n template\n struct depth : std::integral_constant {};\n template\n struct is_wrappable;\n template\n struct is_wrappable : std::false_type {};\n template\n struct is_wrappable : std::false_type {};\n template\n struct is_wrappable : std::integral_constant::is_specialized\n && !std::is_floating_point::value\n && !std::is_same, from_value_t>::value\n && (depth::value < depth::value)> {};\n template\n struct binary_operator<\n Operator, Lhs, Rhs,\n enable_if_t::value && is_derived_from_number_base::value>> {\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(Operator()(lhs, static_cast(rhs)))\n {\n return Operator()(lhs, static_cast(rhs));\n }\n };\n template\n struct binary_operator<\n Operator, Lhs, Rhs,\n enable_if_t::value && std::is_floating_point::value>> {\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(Operator()(static_cast(lhs), rhs))\n {\n return Operator()(static_cast(lhs), rhs);\n }\n };\n template\n struct binary_operator<\n Operator, Lhs, Rhs,\n enable_if_t::value && is_derived_from_number_base::value>> {\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(Operator()(from_value(lhs), rhs)) {\n return Operator()(from_value(lhs), rhs);\n }\n };\n template\n struct binary_operator<\n Operator, Lhs, Rhs,\n enable_if_t::value && is_wrappable::value>> {\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(Operator()(lhs, from_value(rhs)))\n {\n return Operator()(lhs, from_value(rhs));\n }\n };\n template\n struct wants_generic_ops::value>> : std::true_type {\n };\n }\n template\n struct is_composite::value>> : std::true_type {\n };\n namespace _impl {\n template\n struct get_rep;\n template\n using get_rep_t = typename get_rep::type;\n template\n struct set_rep;\n template\n using set_rep_t = typename set_rep::type;\n }\n template\n struct make_signed::value>> {\n using type = _impl::set_rep_t>>;\n };\n template\n struct make_unsigned::value>> {\n using type = _impl::set_rep_t>>;\n };\n namespace _impl {\n template\n constexpr Rep to_rep(number_base const& number) {\n return number._rep;\n }\n }\n template\n struct shift> {\n using _scalar_type = _impl::number_base;\n constexpr auto operator()(_scalar_type const &s) const\n -> decltype(from_rep{}(_impl::shift(to_rep(s))))\n {\n return from_rep{}(_impl::shift(to_rep(s)));\n }\n };\n template\n struct numeric_limits>\n : numeric_limits {\n using _value_type = Derived;\n using _rep = typename _value_type::rep;\n using _rep_numeric_limits = numeric_limits<_rep>;\n static constexpr _value_type min() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::min());\n }\n static constexpr _value_type max() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::max());\n }\n static constexpr _value_type lowest() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::lowest());\n }\n static constexpr _value_type epsilon() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::round_error());\n }\n static constexpr _value_type round_error() noexcept\n {\n return static_cast<_value_type>(_rep_numeric_limits::round_error());\n }\n static constexpr _value_type infinity() noexcept\n {\n return static_cast<_value_type>(_rep_numeric_limits::infinity());\n }\n static constexpr _value_type quiet_NaN() noexcept\n {\n return static_cast<_value_type>(_rep_numeric_limits::quiet_NaN());\n }\n static constexpr _value_type signaling_NaN() noexcept\n {\n return static_cast<_value_type>(_rep_numeric_limits::signaling_NaN());\n }\n static constexpr _value_type denorm_min() noexcept\n {\n return static_cast<_value_type>(_rep_numeric_limits::denorm_min());\n }\n };\n}\nnamespace cnl {\n template\n class elastic_integer;\n namespace _elastic_integer_impl {\n template\n struct is_elastic_integer : std::false_type {\n };\n template\n struct is_elastic_integer> : std::true_type {\n };\n template\n using rep_t = typename set_digits::value, Digits)>::type;\n template\n using base_class_t = _impl::number_base<\n elastic_integer,\n _elastic_integer_impl::rep_t>;\n }\n template\n struct digits> : std::integral_constant<_digits_type, Digits> {\n };\n template\n struct set_digits, MinNumBits> {\n using type = elastic_integer;\n };\n template\n constexpr auto to_rep(elastic_integer const& number)\n -> typename elastic_integer::rep\n {\n using base_type = typename elastic_integer::_base;\n return to_rep(static_cast(number));\n }\n namespace _impl {\n template\n struct get_rep> {\n using type = Narrowest;\n };\n template\n struct set_rep, NewNarrowest> {\n using type = elastic_integer;\n };\n }\n template\n struct from_rep> {\n template\n constexpr auto operator()(Rep const& r) const\n -> elastic_integer::value>>\n {\n return r;\n }\n };\n template\n struct from_value, Value> {\n using type = elastic_integer::value, cnl::_impl::make_signed_t::value>>;\n };\n namespace _elastic_integer_impl {\n template\n constexpr int digits(Integer value) {\n return used_bits((value<0)?-value:value);\n }\n }\n template\n struct from_value, constant> {\n static constexpr auto _to_digits = _elastic_integer_impl::digits(Value);\n using type = elastic_integer<_to_digits, Narrowest>;\n };\n template\n struct scale> {\n constexpr auto operator()(elastic_integer const& s) const\n -> elastic_integer\n {\n using result_type = elastic_integer;\n using result_rep = typename result_type::rep;\n return to_rep(s) * (result_rep{1} << ShiftDigits);\n }\n };\n template\n struct shift, _impl::enable_if_t<0 <= ShiftDigits>> {\n constexpr auto operator()(elastic_integer const& s) const\n -> elastic_integer\n {\n using result_type = elastic_integer;\n using result_rep = typename result_type::rep;\n return to_rep(s) * (result_rep{1} << ShiftDigits);\n }\n };\n template\n struct shift, _impl::enable_if_t> {\n constexpr auto operator()(elastic_integer const& s) const\n -> elastic_integer\n {\n using divisor_type = elastic_integer<1-ShiftDigits, ScalarNarrowest>;\n using divisor_rep = typename divisor_type::rep;\n return to_rep(s) / (divisor_rep{1} << -ShiftDigits);\n }\n };\n template::value, class Narrowest = int>\n class elastic_integer : public _elastic_integer_impl::base_class_t {\n static_assert(Digits > 0, \"type requires positive number of digits\");\n public:\n using _base = _elastic_integer_impl::base_class_t;\n static_assert(!_elastic_integer_impl::is_elastic_integer::value,\n \"elastic_integer of elastic_integer is not a supported\");\n using rep = typename _base::rep;\n constexpr elastic_integer() = default;\n template::is_specialized, int> Dummy = 0>\n constexpr elastic_integer(Number n)\n : _base(static_cast(n))\n {\n }\n template\n explicit constexpr elastic_integer(elastic_integer const& rhs)\n :_base(static_cast(to_rep(rhs)))\n {\n }\n template< ::cnl::intmax Value>\n constexpr elastic_integer(constant)\n : _base(static_cast(Value))\n {\n }\n template::value, int> Dummy = 0>\n elastic_integer& operator=(S s)\n {\n _base::operator=(floating_point_to_rep(s));\n return *this;\n }\n template\n explicit constexpr operator S() const\n {\n return static_cast(to_rep(*this));\n }\n };\n namespace _elastic_integer_impl {\n template\n struct machine_digits {\n static constexpr _digits_type value =\n cnl::digits::type>::value;\n };\n template\n using narrowest = set_digits_t::value>::value>;\n }\n template\n elastic_integer(S const& s)\n -> elastic_integer, _elastic_integer_impl::narrowest>;\n template< ::cnl::intmax Value>\n elastic_integer(constant)\n -> elastic_integer<_elastic_integer_impl::digits(Value)>;\n template< ::cnl::intmax Value>\n constexpr auto make_elastic_integer(constant)\n -> elastic_integer<_elastic_integer_impl::digits(Value)>\n {\n return elastic_integer<_elastic_integer_impl::digits(Value)>{Value};\n }\n namespace _elastic_integer_impl {\n template\n struct make_narrowest {\n using type = Narrowest;\n };\n template\n struct make_narrowest {\n using type = narrowest;\n };\n template\n using make_narrowest_t = typename make_narrowest::type;\n template\n using make_type = elastic_integer::value, make_narrowest_t>;\n }\n template::value, int> Dummy = 0>\n constexpr auto make_elastic_integer(Integral const& value)\n -> _elastic_integer_impl::make_type\n {\n return _elastic_integer_impl::make_type{value};\n }\n template\n constexpr auto operator~(elastic_integer const& rhs)\n -> elastic_integer\n {\n using elastic_integer = elastic_integer;\n using rep = typename elastic_integer::rep;\n return from_rep{}(\n static_cast(\n to_rep(rhs)\n ^ ((static_cast(~0)) >> (numeric_limits::digits - RhsDigits))));\n }\n namespace _impl {\n template::value, std::nullptr_t> Dummy = nullptr>\n constexpr auto cast_to_common_type(\n elastic_integer const& from,\n elastic_integer const&)\n -> decltype(static_cast<_impl::common_type_t<\n elastic_integer,\n elastic_integer>>(from)) {\n return static_cast<_impl::common_type_t<\n elastic_integer,\n elastic_integer>>(from);\n }\n template\n struct binary_operator, elastic_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n elastic_integer const& lhs,\n elastic_integer const& rhs) const\n -> decltype(Operator()(cast_to_common_type(lhs, rhs), cast_to_common_type(rhs, lhs)))\n {\n return Operator()(cast_to_common_type(lhs, rhs), cast_to_common_type(rhs, lhs));\n }\n };\n template\n struct binary_operator, elastic_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n elastic_integer const& lhs,\n elastic_integer const& rhs) const\n -> decltype(Operator()(to_rep(lhs), to_rep(rhs)))\n {\n return Operator()(to_rep(lhs), to_rep(rhs));\n }\n };\n template\n struct policy;\n template\n struct policy<_impl::add_op, LhsTraits, RhsTraits> {\n static constexpr int digits = _impl::max(LhsTraits::digits, RhsTraits::digits)+1;\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::subtract_op, LhsTraits, RhsTraits> {\n static constexpr int digits = _impl::max(LhsTraits::digits, RhsTraits::digits) + (LhsTraits::is_signed | RhsTraits::is_signed);\n static constexpr bool is_signed = true;\n };\n template\n struct policy<_impl::multiply_op, LhsTraits, RhsTraits> {\n static constexpr int contribution(int operand_digits) { return operand_digits == 1 ? 0 : operand_digits; }\n static constexpr int digits = max(1, contribution(LhsTraits::digits)+contribution(RhsTraits::digits));\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::divide_op, LhsTraits, RhsTraits> {\n static constexpr int digits = LhsTraits::digits;\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::bitwise_or_op, LhsTraits, RhsTraits> {\n static constexpr int digits = _impl::max(LhsTraits::digits, RhsTraits::digits);\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::bitwise_and_op, LhsTraits, RhsTraits> {\n static constexpr int digits = _impl::min(LhsTraits::digits, RhsTraits::digits);\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::bitwise_xor_op, LhsTraits, RhsTraits> {\n static constexpr int digits = _impl::max(LhsTraits::digits, RhsTraits::digits);\n static constexpr bool is_signed = LhsTraits::is_signed || RhsTraits::is_signed;\n };\n template\n struct policy<_impl::shift_left_op, LhsTraits, RhsTraits> {\n static constexpr int digits = LhsTraits::digits;\n static constexpr bool is_signed = LhsTraits::is_signed;\n };\n template\n struct policy<_impl::shift_right_op, LhsTraits, RhsTraits> {\n static constexpr int digits = LhsTraits::digits;\n static constexpr bool is_signed = LhsTraits::is_signed;\n };\n template\n struct operate_params {\n using lhs = elastic_integer;\n using rhs = elastic_integer;\n using lhs_traits = numeric_limits;\n using rhs_traits = numeric_limits;\n using policy = typename _impl::policy;\n using lhs_rep = typename lhs::rep;\n using rhs_rep = typename rhs::rep;\n using rep_result = typename _impl::op_result;\n static constexpr _digits_type narrowest_width = _impl::max(\n digits::value + cnl::is_signed::value,\n digits::value + cnl::is_signed::value);\n using narrowest = set_digits_t<_impl::make_signed_t, narrowest_width-policy::is_signed>;\n using result_type = elastic_integer;\n };\n template\n struct binary_operator, elastic_integer,\n typename Operator::is_not_comparison> {\n constexpr auto operator()(\n elastic_integer const& lhs,\n elastic_integer const& rhs) const\n -> typename operate_params::result_type\n {\n using result_type = typename operate_params::result_type;\n return from_rep{}(\n static_cast(Operator()(\n to_rep(static_cast(lhs)),\n to_rep(static_cast(rhs)))));\n }\n };\n }\n template\n constexpr auto operator<<(elastic_integer const& lhs, constant)\n -> decltype(from_rep(RhsValue), LhsNarrowest>>{}(\n to_rep(static_cast(RhsValue), LhsNarrowest>>(lhs)) << RhsValue)) {\n using result_type = elastic_integer(RhsValue), LhsNarrowest>;\n return from_rep{}(to_rep(static_cast(lhs)) << RhsValue);\n }\n template\n constexpr auto operator>>(elastic_integer const& lhs, constant)\n -> decltype (from_rep(RhsValue), LhsNarrowest>>{}(to_rep(lhs) >> RhsValue)) {\n return from_rep(RhsValue), LhsNarrowest>>{}(to_rep(lhs) >> RhsValue);\n }\n template\n constexpr auto operator-(elastic_integer const& rhs)\n -> decltype(from_rep::type>>{}(-to_rep(static_cast::type>>(rhs))))\n {\n using result_type = elastic_integer::type>;\n return from_rep{}(-to_rep(static_cast(rhs)));\n }\n template\n constexpr auto operator+(elastic_integer const& rhs)\n -> decltype(from_rep::type>>{}(\n to_rep(static_cast::type>>(rhs))))\n {\n using result_type = elastic_integer::type>;\n return from_rep{}(to_rep(static_cast(rhs)));\n }\n}\nnamespace std {\n template\n struct common_type, cnl::elastic_integer> {\n using type = cnl::elastic_integer<\n cnl::_impl::max(LhsDigits, RhsDigits),\n cnl::_impl::common_signedness_t>;\n };\n template\n struct common_type, Rhs>\n : common_type, cnl::elastic_integer::digits, Rhs>> {\n };\n template\n struct common_type>\n : common_type::digits, Lhs>, cnl::elastic_integer> {\n };\n}\nnamespace cnl {\n namespace _elastic_integer_impl {\n template\n struct lowest;\n template\n struct lowest {\n constexpr Rep operator()(Rep const& max) const noexcept\n {\n return static_cast(-max);\n }\n };\n template\n struct lowest {\n constexpr Rep operator()(Rep const&) const noexcept\n {\n return 0;\n }\n };\n }\n template\n struct numeric_limits>\n : numeric_limits {\n using _narrowest_numeric_limits = numeric_limits;\n using _value_type = elastic_integer;\n using _rep = typename _value_type::rep;\n using _rep_numeric_limits = numeric_limits<_rep>;\n static constexpr _rep _rep_max() noexcept\n {\n return static_cast<_rep>(_rep_numeric_limits::max() >> (_rep_numeric_limits::digits-digits));\n }\n static constexpr int digits = Digits;\n static constexpr _value_type min() noexcept\n {\n return from_rep<_value_type>{}(1);\n }\n static constexpr _value_type max() noexcept\n {\n return from_rep<_value_type>{}(_rep_max());\n }\n static constexpr _value_type lowest() noexcept\n {\n return _elastic_integer_impl::lowest<_rep, _narrowest_numeric_limits::is_signed>()(_rep_max());\n }\n };\n template\n struct numeric_limits const>\n : numeric_limits> {\n };\n}\nnamespace cnl {\n template\n class fixed_point;\n template\n constexpr Rep to_rep(fixed_point const&);\n template\n struct fractional;\n namespace _impl {\n template\n struct is_fixed_point\n : public std::false_type {\n };\n template\n struct is_fixed_point>\n : public std::true_type {\n };\n namespace fp {\n template\n struct float_of_size;\n template\n struct float_of_size> {\n using type = float;\n };\n template\n struct float_of_size> {\n using type = double;\n };\n template\n struct float_of_size> {\n using type = long double;\n };\n template\n using float_of_same_size = typename float_of_size::value + is_signed::value>::type;\n }\n }\n template\n class fixed_point\n : public _impl::number_base, Rep> {\n static_assert(!_impl::is_fixed_point::value,\n \"fixed_point of fixed_point is not a supported\");\n public:\n using rep = Rep;\n using _base = _impl::number_base, Rep>;\n constexpr static int exponent = Exponent;\n private:\n constexpr fixed_point(rep r, int)\n :_base(r)\n {\n }\n public:\n constexpr fixed_point() = default;\n template\n constexpr fixed_point(fixed_point const& rhs)\n : _base(\n static_cast(_impl::shift(_impl::from_value(cnl::to_rep(rhs)))))\n {\n }\n template< ::cnl::intmax Value>\n constexpr fixed_point(constant)\n : fixed_point(from_rep>{}(Value))\n {\n }\n template::is_integer, int> Dummy = 0>\n constexpr fixed_point(S const& s)\n : _base(static_cast(_impl::shift<-exponent>(_impl::from_value(s))))\n {\n }\n template::is_iec559, int> Dummy = 0>\n constexpr fixed_point(S s)\n :_base(floating_point_to_rep(s))\n {\n }\n template\n constexpr fixed_point(fractional const& f);\n template::is_iec559, int> Dummy = 0>\n constexpr fixed_point& operator=(S s)\n {\n _base::operator=(floating_point_to_rep(s));\n return *this;\n }\n template\n constexpr fixed_point& operator=(fixed_point const& rhs)\n {\n _base::operator=(fixed_point_to_rep(rhs));\n return *this;\n }\n template::is_integer, int> Dummy = 0>\n explicit constexpr operator S() const\n {\n return static_cast(_impl::shift(to_rep(*this)));\n }\n template::is_iec559, int> Dummy = 0>\n explicit constexpr operator S() const\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return S(to_rep(*this))*inverse_one();\n }\n template\n friend struct from_rep;\n private:\n template::is_iec559, int> Dummy = 0>\n static constexpr S one();\n template::is_integer, int> Dummy = 0>\n static constexpr S one();\n template\n static constexpr S inverse_one();\n template\n static constexpr S rep_to_integral(rep r);\n template\n static constexpr rep floating_point_to_rep(S s);\n template\n static constexpr S rep_to_floating_point(rep r);\n template\n static constexpr rep fixed_point_to_rep(fixed_point const& rhs);\n };\n template\n constexpr int fixed_point::exponent;\n template< ::cnl::intmax Value>\n fixed_point(::cnl::constant)\n -> fixed_point::value, used_bits(Value)-trailing_bits(Value))>, trailing_bits(Value)>;\n template\n fixed_point(Integer)\n -> fixed_point;\n namespace _impl {\n namespace fp {\n namespace type {\n template Dummy = 0>\n constexpr S pow2()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return S{1.};\n }\n template Dummy = 0>\n constexpr S pow2()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return pow2()*S(2);\n }\n template=8), int> Dummy = 0>\n constexpr S pow2()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return pow2()*S(256);\n }\n template=0) && (Exponent>-8), int> Dummy = 0>\n constexpr S pow2()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return pow2()*S(.5);\n }\n template Dummy = 0>\n constexpr S pow2()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return pow2()*S(.003906250);\n }\n }\n }\n }\n template\n template::is_iec559, int> Dummy>\n constexpr S fixed_point::one()\n {\n return _impl::fp::type::pow2();\n }\n template\n template::is_integer, int> Dummy>\n constexpr S fixed_point::one()\n {\n return from_rep>{}(1);\n }\n template\n template\n constexpr S fixed_point::inverse_one()\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return _impl::fp::type::pow2();\n }\n template\n template\n constexpr typename fixed_point::rep fixed_point::floating_point_to_rep(S s)\n {\n static_assert(numeric_limits::is_iec559, \"S must be floating-point type\");\n return static_cast(s*one());\n }\n template\n template\n constexpr typename fixed_point::rep fixed_point::fixed_point_to_rep(fixed_point const& rhs)\n {\n return _impl::shift(to_rep(rhs));\n }\n}\nnamespace cnl {\n namespace _impl {\n template \n struct get_rep> {\n using type = Rep;\n };\n template \n struct set_rep, NewRep> {\n using type = fixed_point;\n };\n }\n template \n struct digits> : digits {\n };\n template \n struct set_digits, MinNumBits> {\n using type = fixed_point, Exponent>;\n };\n template\n struct from_rep> {\n template\n constexpr auto operator()(Rep const& r) const\n -> fixed_point {\n return fixed_point(r, 0);\n }\n };\n template\n constexpr Rep to_rep(fixed_point const& number)\n {\n using base_type = typename fixed_point::_base;\n return to_rep(static_cast(number));\n }\n template \n struct from_value, Value> {\n using type = fixed_point;\n };\n template \n struct from_value, fixed_point> {\n using type = fixed_point, ValueExponent>;\n };\n template\n struct from_value, constant> {\n using type = fixed_point<\n set_digits_t::value, used_bits(Value)-trailing_bits(Value))>,\n trailing_bits(Value)>;\n };\n namespace _impl {\n template \n struct fractional_digits : std::integral_constant<_digits_type, 0> {\n };\n template \n struct fractional_digits> : std::integral_constant<_digits_type, -Exponent> {\n };\n template \n struct integer_digits : std::integral_constant<_digits_type, digits::value - fractional_digits::value> {\n };\n }\n}\nnamespace cnl {\n template\n constexpr auto make_fixed_point(Value const& value)\n -> cnl::from_value_t, Value>\n {\n return _impl::from_value>(value);\n }\n namespace _multiply_impl {\n template\n struct fixed_point_type {\n using type = fixed_point;\n };\n template\n struct fixed_point_type> {\n using type = fixed_point;\n };\n template\n struct params {\n using lhs_type = typename fixed_point_type::type;\n using rhs_type = typename fixed_point_type::type;\n using lhs_rep = typename lhs_type::rep;\n using rhs_rep = typename rhs_type::rep;\n static constexpr int rep_exponent = lhs_type::exponent + rhs_type::exponent;\n using rep_op_result = _impl::op_result<_impl::multiply_op, lhs_rep, rhs_rep>;\n static constexpr int sum_digits = digits::value + digits::value;\n static constexpr bool is_signed =\n numeric_limits::is_signed || numeric_limits::is_signed;\n using prewidened_result_rep = _impl::make_signed_t;\n using result_rep = set_digits_t;\n using rep_type = typename std::conditional<\n digits::value >= sum_digits,\n lhs_rep, result_rep>::type;\n using result_type = fixed_point;\n using intermediate_lhs = fixed_point;\n using intermediate_rhs = Rhs;\n };\n }\n template\n constexpr auto multiply(Lhs const& lhs, Rhs const& rhs)\n -> typename _multiply_impl::params::result_type\n {\n using params = _multiply_impl::params;\n using intermediate_lhs = typename params::intermediate_lhs;\n using intermediate_rhs = typename params::intermediate_rhs;\n using result_type = typename params::result_type;\n using result_rep = typename result_type::rep;\n return from_rep{}(\n static_cast(to_rep(static_cast(lhs))\n * to_rep(static_cast(rhs))));\n }\n namespace _divide_impl {\n template\n struct divide;\n }\n template\n constexpr auto divide(Lhs const& lhs, Rhs const& rhs)\n -> decltype(_divide_impl::divide()(lhs, rhs)) {\n return _divide_impl::divide()(lhs, rhs);\n }\n namespace _divide_impl {\n template\n struct params {\n using lhs_rep = typename Lhs::rep;\n using rhs_rep = typename Rhs::rep;\n using rep_op_result = _impl::op_result<_impl::divide_op, lhs_rep, rhs_rep>;\n static constexpr int integer_digits =\n _impl::integer_digits::value + _impl::fractional_digits::value;\n static constexpr int fractional_digits =\n _impl::fractional_digits::value + _impl::integer_digits::value;\n static constexpr int necessary_digits = integer_digits + fractional_digits;\n static constexpr bool is_signed =\n numeric_limits::is_signed || numeric_limits::is_signed;\n static constexpr int promotion_digits = digits::value;\n static constexpr int max_digits = _impl::max(necessary_digits, promotion_digits);\n using prewidened_result_rep = _impl::make_signed_t;\n using rep_type = set_digits_t;\n static constexpr int rep_exponent = -fractional_digits;\n static constexpr int intermediate_exponent_lhs = Lhs::exponent - digits::value;\n using result_type = fixed_point;\n };\n template\n struct divide, fixed_point> {\n constexpr auto operator()(fixed_point const& lhs, fixed_point const& rhs) const\n -> typename params, fixed_point>::result_type {\n using params = params, fixed_point>;\n using result_type = typename params::result_type;\n using result_rep = typename result_type::rep;\n return from_rep{}(static_cast(_impl::scale::value>(\n static_cast(to_rep(lhs)))/to_rep(rhs)));\n }\n };\n template\n struct divide> {\n constexpr auto operator()(Lhs const& lhs, fixed_point const& rhs) const\n -> decltype(cnl::divide(make_fixed_point(lhs), rhs))\n {\n return cnl::divide(make_fixed_point(lhs), rhs);\n }\n };\n template\n struct divide, Rhs> {\n constexpr auto operator()(fixed_point const& lhs, Rhs const& rhs) const\n -> decltype(cnl::divide(lhs, make_fixed_point(rhs)))\n {\n return cnl::divide(lhs, make_fixed_point(rhs));\n }\n };\n template\n struct divide {\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(cnl::divide(make_fixed_point(lhs), make_fixed_point(rhs)))\n {\n return cnl::divide(make_fixed_point(lhs), make_fixed_point(rhs));\n }\n };\n }\n}\nnamespace cnl {\n template\n struct fractional {\n using numerator_type = Numerator;\n using denominator_type = Denominator;\n explicit constexpr fractional(Numerator const& n, Denominator const& d)\n : numerator{n}, denominator{d} {}\n explicit constexpr fractional(Numerator const& n)\n : numerator{n}, denominator{1} {}\n template::value, int> = 0>\n explicit constexpr operator Scalar() const\n {\n return static_cast(numerator)/static_cast(denominator);\n }\n numerator_type numerator;\n denominator_type denominator = 1;\n };\n template\n fractional(Numerator const& n, Denominator const& d)\n -> fractional;\n template\n fractional(Numerator const& n)\n -> fractional;\n template\n constexpr fractional make_fractional(Numerator const& n, Denominator const& d)\n {\n return fractional{n, d};\n }\n template\n constexpr fractional make_fractional(Numerator const& n)\n {\n return fractional{n, 1};\n }\n template\n constexpr auto operator+(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(make_fractional(\n lhs.numerator*rhs.denominator+rhs.numerator*lhs.denominator, lhs.denominator*rhs.denominator))\n {\n return make_fractional(\n lhs.numerator*rhs.denominator+rhs.numerator*lhs.denominator, lhs.denominator*rhs.denominator);\n }\n template\n constexpr auto operator-(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(make_fractional(\n lhs.numerator*rhs.denominator-rhs.numerator*lhs.denominator, lhs.denominator*rhs.denominator))\n {\n return make_fractional(\n lhs.numerator*rhs.denominator-rhs.numerator*lhs.denominator, lhs.denominator*rhs.denominator);\n }\n template\n constexpr auto operator*(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(make_fractional(lhs.numerator*rhs.numerator, lhs.denominator*rhs.denominator))\n {\n return make_fractional(lhs.numerator*rhs.numerator, lhs.denominator*rhs.denominator);\n }\n template\n constexpr auto operator/(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(make_fractional(lhs.numerator*rhs.denominator, lhs.denominator*rhs.numerator))\n {\n return make_fractional(lhs.numerator*rhs.denominator, lhs.denominator*rhs.numerator);\n }\n namespace _fractional_impl {\n template\n constexpr auto one(fractional const& f)\n -> decltype(f.numerator==f.denominator)\n {\n return f.numerator==f.denominator;\n }\n }\n template\n constexpr auto operator==(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(_fractional_impl::one(lhs/rhs))\n {\n return _fractional_impl::one(lhs/rhs);\n }\n template\n constexpr auto operator!=(\n fractional const& lhs,\n fractional const& rhs)\n -> decltype(!(lhs==rhs))\n {\n return !(lhs==rhs);\n }\n}\nnamespace cnl {\n template\n constexpr auto make_fixed_point(fractional const& value)\n -> decltype(divide(value.numerator, value.denominator))\n {\n return divide(value.numerator, value.denominator);\n }\n template\n template\n constexpr fixed_point::fixed_point(fractional const& f)\n : fixed_point(divide(f.numerator, f.denominator))\n {\n }\n template\n fixed_point(fractional)\n -> fixed_point<\n typename decltype(cnl::divide(std::declval(), std::declval()))::rep,\n decltype(cnl::divide(std::declval(), std::declval()))::exponent>;\n}\nnamespace cnl {\n namespace _impl {\n namespace fp {\n namespace ct {\n template\n struct common_type_mixed;\n template\n struct common_type_mixed, RhsInteger, _impl::enable_if_t::is_integer>> : std::common_type<\n fixed_point, fixed_point> {\n };\n template\n struct common_type_mixed<\n fixed_point, Float,\n _impl::enable_if_t::value>>\n : std::common_type<_impl::fp::float_of_same_size, Float> {\n };\n }\n }\n }\n}\nnamespace std {\n template\n struct common_type> {\n using type = cnl::fixed_point<\n typename std::common_type::type,\n Exponent>;\n };\n template\n struct common_type, Rhs> {\n static_assert(!cnl::_impl::is_fixed_point::value, \"fixed-point Rhs type\");\n using type = typename cnl::_impl::fp::ct::common_type_mixed, Rhs>::type;\n };\n template\n struct common_type> {\n static_assert(!cnl::_impl::is_fixed_point::value, \"fixed-point Lhs type\");\n using type = typename cnl::_impl::fp::ct::common_type_mixed, Lhs>::type;\n };\n template\n struct common_type, cnl::fixed_point> {\n using type = cnl::fixed_point, cnl::_impl::min(LhsExponent, RhsExponent)>;\n };\n}\nnamespace cnl {\n namespace _impl {\n template\n constexpr auto pi(int const max_iterations) {\n using fp = fixed_point;\n constexpr auto four = fixed_point::value>{4.};\n auto previous = fp{3.};\n for(auto n = 2; n != (max_iterations << 1); n += 4) {\n auto const addend = four / ((n+0L) * (n+1L) * (n+2L));\n auto const subtrahend = four / ((n+2L) * (n+3L) * (n+4L));\n auto next = fp{previous + addend - subtrahend};\n if (next == previous) {\n return next;\n }\n previous = next;\n }\n return previous;\n }\n template\n constexpr auto pi() {\n return pi(0);\n }\n template\n constexpr auto e(int const max_iterations) {\n using fp = fixed_point;\n constexpr auto one = fixed_point::value>{1.};\n auto previous = fp{2.};\n auto factor = 2;\n for (auto n = 2; n != max_iterations; ++ n, factor *= n) {\n auto const addend = one / factor;\n auto next = fp{previous + addend};\n if (next == previous) {\n return next;\n }\n previous = next;\n }\n return previous;\n }\n template\n constexpr auto e() {\n return e(0);\n }\n template\n constexpr auto constant_with_fallback(Float constant, fixed_point(*procedure)()) {\n using fp = fixed_point;\n auto const required_integer_digits = used_bits(static_cast(constant));\n constexpr auto fixed_fractional_digits = fractional_digits::value;\n constexpr auto float_digits = std::numeric_limits::digits;\n auto const float_fractional_digits = float_digits - required_integer_digits;\n return (float_fractional_digits >= fixed_fractional_digits)\n ? fp{constant}\n : procedure();\n }\n }\n namespace math_constants {\n template inline constexpr fixed_point e> {\n _impl::constant_with_fallback(e, _impl::e)\n };\n template inline constexpr fixed_point log2e> {\n fixed_point{ log2e }\n };\n template inline constexpr fixed_point log10e> {\n fixed_point{ log10e }\n };\n template inline constexpr fixed_point pi>{\n _impl::constant_with_fallback(pi, _impl::pi)\n };\n template inline constexpr fixed_point invpi> {\n fixed_point{ invpi }\n };\n template inline constexpr fixed_point invsqrtpi> {\n fixed_point{ invsqrtpi }\n };\n template inline constexpr fixed_point ln2> {\n fixed_point{ ln2 }\n };\n template inline constexpr fixed_point ln10> {\n fixed_point{ ln10 }\n };\n template inline constexpr fixed_point sqrt2> {\n fixed_point{ sqrt2 }\n };\n template inline constexpr fixed_point sqrt3> {\n fixed_point{ sqrt3 }\n };\n template inline constexpr fixed_point invsqrt2> {\n fixed_point{ invsqrt2 }\n };\n template inline constexpr fixed_point invsqrt3> {\n fixed_point{ invsqrt3 }\n };\n template inline constexpr fixed_point radian> {\n fixed_point{ radian }\n };\n template inline constexpr fixed_point egamma> {\n fixed_point{ egamma }\n };\n template inline constexpr fixed_point phi> {\n fixed_point{ phi }\n };\n template inline constexpr fixed_point catalan> {\n fixed_point{ catalan }\n };\n template inline constexpr fixed_point apery> {\n fixed_point{ apery }\n };\n template inline constexpr fixed_point glaisher> {\n fixed_point{ glaisher }\n };\n }\n}\nnamespace cnl {\n namespace _fixed_point_operators_impl {\n template\n constexpr bool is_heterogeneous() {\n return (!std::is_same::value) &&\n (_impl::is_fixed_point::value || _impl::is_fixed_point::value);\n }\n }\n namespace _impl {\n template\n struct unary_operator> {\n constexpr auto operator()(fixed_point const& rhs) const\n -> decltype(from_rep>{}(Operator()(to_rep(rhs))))\n {\n return from_rep>{}(Operator()(to_rep(rhs)));\n }\n };\n template\n struct binary_operator, fixed_point,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n fixed_point const& lhs,\n fixed_point const& rhs) const\n -> decltype(Operator()(to_rep(lhs), to_rep(rhs)))\n {\n return Operator()(to_rep(lhs), to_rep(rhs));\n }\n };\n template\n struct binary_operator, fixed_point,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n fixed_point const& lhs,\n fixed_point const& rhs) const\n -> decltype(Operator()(static_cast<_impl::common_type_t, fixed_point>>(lhs), static_cast<_impl::common_type_t, fixed_point>>(rhs)))\n {\n using common_type = _impl::common_type_t, fixed_point>;\n return Operator()(static_cast(lhs), static_cast(rhs));\n }\n };\n template\n struct binary_operator, fixed_point> {\n constexpr auto operator()(\n fixed_point const& lhs,\n fixed_point const& rhs) const\n -> decltype(from_rep>{}(to_rep(lhs)*to_rep(rhs)))\n {\n return from_rep>{}(to_rep(lhs)*to_rep(rhs));\n }\n };\n template\n struct binary_operator, fixed_point> {\n constexpr auto operator()(\n fixed_point const& lhs,\n fixed_point const& rhs) const\n -> decltype(from_rep>{}(to_rep(lhs)\n /to_rep(rhs)))\n {\n return from_rep>{}(to_rep(lhs)\n /to_rep(rhs));\n }\n };\n template\n struct binary_operator, fixed_point> {\n constexpr auto operator()(\n fixed_point const& lhs,\n fixed_point const& rhs) const\n -> decltype(from_rep>{}(to_rep(lhs)%to_rep(rhs)))\n {\n return from_rep>{}(to_rep(lhs)%to_rep(rhs));\n }\n };\n template struct is_zero_degree : std::true_type {};\n template<> struct is_zero_degree : std::false_type {};\n template<> struct is_zero_degree : std::false_type {};\n template<> struct is_zero_degree : std::false_type {};\n template<> struct is_zero_degree : std::false_type {};\n template<> struct is_zero_degree : std::false_type {};\n template\n struct binary_operator, fixed_point,\n enable_if_t::value, typename Operator::is_not_comparison>> {\n constexpr auto operator()(\n fixed_point const& lhs, fixed_point const& rhs) const\n -> decltype(from_rep>{}(\n Operator()(to_rep(lhs), to_rep(rhs))))\n {\n return from_rep>{}(\n Operator()(to_rep(lhs), to_rep(rhs)));\n }\n };\n template\n struct binary_operator, fixed_point,\n enable_if_t::value, typename Operator::is_not_comparison>> {\n private:\n static constexpr int _common_exponent = min(LhsExponent, RhsExponent);\n static constexpr int _lhs_left_shift = LhsExponent-_common_exponent;\n static constexpr int _rhs_left_shift = RhsExponent-_common_exponent;\n public:\n constexpr auto operator()(\n fixed_point const& lhs, fixed_point const& rhs) const\n -> decltype(Operator{}(\n from_rep>{}(\n _impl::shift<_lhs_left_shift>(to_rep(lhs))),\n from_rep>{}(\n _impl::shift<_rhs_left_shift>(to_rep(rhs)))))\n {\n return Operator{}(\n from_rep>{}(\n _impl::shift<_lhs_left_shift>(to_rep(lhs))),\n from_rep>{}(\n _impl::shift<_rhs_left_shift>(to_rep(rhs))));\n }\n };\n }\n template\n constexpr auto operator<<(fixed_point const& lhs, Rhs const& rhs)\n -> decltype(from_rep>{}(to_rep(lhs) << int(rhs)))\n {\n return from_rep>{}(to_rep(lhs) << int(rhs));\n }\n template\n constexpr auto operator>>(fixed_point const& lhs, Rhs const& rhs)\n -> decltype(from_rep> int(rhs)), LhsExponent>>{}(to_rep(lhs) >> int(rhs)))\n {\n return from_rep> int(rhs)), LhsExponent>>{}(to_rep(lhs) >> int(rhs));\n }\n template\n constexpr fixed_point(RhsValue)>\n operator<<(fixed_point const& lhs, constant)\n {\n return from_rep(RhsValue)>>{}(to_rep(lhs));\n }\n template\n constexpr fixed_point(RhsValue)>\n operator>>(fixed_point const& lhs, constant)\n {\n return from_rep(RhsValue)>>{}(to_rep(lhs));\n }\n}\n \nnamespace cnl {\n template\n constexpr auto abs(fixed_point const& x) noexcept\n -> decltype(-x)\n {\n return (x >= 0) ? static_cast(x) : -x;\n }\n namespace _impl {\n namespace fp {\n namespace extras {\n template\n constexpr Rep sqrt_bit(Rep n, Rep bit)\n {\n return (bit>n) ? sqrt_bit(n, static_cast(bit >> 2)) : bit;\n }\n template\n constexpr Rep sqrt_bit(Rep n)\n {\n return sqrt_bit(n, Rep(1) << (Rep((digits::value + is_signed::value) - 2)));\n }\n template\n constexpr Rep sqrt_solve3(\n Rep n,\n Rep bit,\n Rep result)\n {\n return (bit!=Rep{0})\n ? (n>=result+bit)\n ? sqrt_solve3(\n static_cast(n-(result+bit)),\n static_cast(bit >> 2),\n static_cast((result >> 1)+bit))\n : sqrt_solve3(\n n,\n static_cast(bit >> 2),\n static_cast(result >> 1))\n : result;\n }\n struct sqrt_solve1 {\n template\n constexpr Rep operator()(Rep n) const\n {\n return sqrt_solve3(n, sqrt_bit(n), Rep{0});\n }\n };\n }\n }\n }\n template\n constexpr fixed_point \n sqrt(fixed_point const& x)\n {\n using widened_rep = set_digits_t::value*2>;\n return\n (x>{}(0))\n ? throw std::invalid_argument(\"cannot represent square root of negative value\") :\n from_rep>{}(_impl::for_rep(\n _impl::fp::extras::sqrt_solve1(),\n _impl::scale<-Exponent>(static_cast(to_rep(x)))));\n }\n namespace _impl {\n namespace fp {\n namespace extras {\n template(* F)(\n _impl::fp::float_of_same_size)>\n constexpr fixed_point \n crib(fixed_point const& x) noexcept\n {\n using floating_point = _impl::fp::float_of_same_size;\n return static_cast>(F(static_cast(x)));\n }\n }\n }\n }\n template\n constexpr fixed_point \n sin(fixed_point const& x) noexcept\n {\n return _impl::fp::extras::crib(x);\n }\n template\n constexpr fixed_point \n cos(fixed_point const& x) noexcept\n {\n return _impl::fp::extras::crib(x);\n }\n template\n constexpr fixed_point \n exp(fixed_point const& x) noexcept\n {\n return _impl::fp::extras::crib(x);\n }\n template\n constexpr fixed_point \n pow(fixed_point const& x) noexcept\n {\n return _impl::fp::extras::crib(x);\n }\n template\n ::std::ostream& operator<<(::std::ostream& out, fixed_point const& fp)\n {\n return out << static_cast(fp);\n }\n template\n ::std::istream& operator>>(::std::istream& in, fixed_point & fp)\n {\n long double ld;\n in >> ld;\n fp = ld;\n return in;\n }\n}\nnamespace cnl {\n template\n struct numeric_limits>\n : numeric_limits, Rep>> {\n using _value_type = cnl::fixed_point;\n using _rep = typename _value_type::rep;\n using _rep_numeric_limits = numeric_limits<_rep>;\n static constexpr _value_type min() noexcept\n {\n return from_rep<_value_type>{}(_rep{1});\n }\n static constexpr _value_type max() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::max());\n }\n static constexpr _value_type lowest() noexcept\n {\n return from_rep<_value_type>{}(_rep_numeric_limits::lowest());\n }\n static constexpr bool is_integer = false;\n static constexpr _value_type epsilon() noexcept\n {\n return from_rep<_value_type>{}(_rep{1});\n }\n static constexpr _value_type round_error() noexcept\n {\n return from_rep<_value_type>{}(_rep{0});\n }\n static constexpr _value_type infinity() noexcept\n {\n return from_rep<_value_type>{}(_rep{0});\n }\n static constexpr _value_type quiet_NaN() noexcept\n {\n return from_rep<_value_type>{}(_rep{0});\n }\n static constexpr _value_type signaling_NaN() noexcept\n {\n return from_rep<_value_type>{}(_rep{0});\n }\n static constexpr _value_type denorm_min() noexcept\n {\n return from_rep<_value_type>{}(_rep{1});\n }\n };\n}\nnamespace std {\n template\n struct numeric_limits>\n : cnl::numeric_limits> {\n };\n template\n struct numeric_limits const>\n : cnl::numeric_limits> {\n };\n}\nnamespace cnl {\n template\n using elastic_number = fixed_point, Exponent>;\n template<\n typename Narrowest = int,\n ::cnl::intmax Value = 0>\n constexpr elastic_number<\n _impl::max(_elastic_integer_impl::digits(Value)-trailing_bits(Value), 1),\n trailing_bits(Value),\n Narrowest>\n make_elastic_number(constant)\n {\n return Value;\n }\n template\n constexpr elastic_number::digits, 0, Narrowest>\n make_elastic_number(Integral value)\n {\n return {value};\n }\n namespace literals {\n template\n constexpr auto operator \"\" _elastic()\n -> decltype(make_elastic_number(\n constant<_cnlint_impl::parse({Chars..., '\\0'})>{}))\n {\n return make_elastic_number(\n constant<_cnlint_impl::parse({Chars..., '\\0'})>{});\n }\n }\n}\nnamespace cnl {\n namespace _impl {\n template\n struct unsigned_or_float;\n template\n struct unsigned_or_float::is_iec559>> {\n using type = T;\n };\n template\n struct unsigned_or_float::is_iec559>> : make_unsigned {\n };\n template\n using unsigned_or_float_t = typename unsigned_or_float::type;\n template\n struct encompasses_signedness\n : std::integral_constant::value >= ::cnl::digits::value> {\n };\n template\n struct encompasses_signedness : std::false_type {\n };\n template\n struct encompasses\n : encompasses_signedness<\n Encompasser, ::cnl::is_signed::value,\n Encompassed, ::cnl::is_signed::value> {\n };\n }\n}\nnamespace cnl {\n static constexpr struct native_overflow_tag {\n } native_overflow{};\n static constexpr struct throwing_overflow_tag {\n } throwing_overflow{};\n static constexpr struct saturated_overflow_tag {\n } saturated_overflow{};\n namespace _overflow_impl {\n template\n constexpr Result return_if(bool condition, Result const& value, char const* )\n {\n return condition ? value : throw std::overflow_error(\"\");\n }\n template\n struct positive_digits : public std::integral_constant::digits> {\n };\n template\n struct negative_digits\n : public std::integral_constant::value ? numeric_limits::digits : 0> {\n };\n template<\n class Destination, class Source,\n _impl::enable_if_t::value::value), int> dummy = 0>\n constexpr bool is_positive_overflow(Source const&)\n {\n return false;\n }\n template<\n class Destination, class Source,\n _impl::enable_if_t<(positive_digits::value::value), int> dummy = 0>\n constexpr bool is_positive_overflow(Source const& source)\n {\n return source>static_cast(numeric_limits::max());\n }\n template<\n class Destination, class Source,\n _impl::enable_if_t::value::value), int> dummy = 0>\n constexpr bool is_negative_overflow(Source const&)\n {\n return false;\n }\n template<\n class Destination, class Source,\n _impl::enable_if_t<(negative_digits::value::value), int> dummy = 0>\n constexpr bool is_negative_overflow(Source const& source)\n {\n return source(numeric_limits::lowest());\n }\n template\n struct binary_operator;\n template\n struct comparison_operator;\n }\n template\n constexpr Result convert(native_overflow_tag, Input const& rhs)\n {\n return static_cast(rhs);\n }\n template\n constexpr Result convert(throwing_overflow_tag, Input const& rhs)\n {\n return _impl::encompasses::value\n ? static_cast(rhs)\n : _overflow_impl::return_if(\n !_overflow_impl::is_positive_overflow(rhs),\n _overflow_impl::return_if(\n !_overflow_impl::is_negative_overflow(rhs),\n static_cast(rhs),\n \"negative overflow in conversion\"),\n \"positive overflow in conversion\");\n }\n template\n constexpr Result convert(saturated_overflow_tag, Input const& rhs)\n {\n using numeric_limits = numeric_limits;\n return !_impl::encompasses::value\n ? _overflow_impl::is_positive_overflow(rhs)\n ? numeric_limits::max()\n : _overflow_impl::is_negative_overflow(rhs)\n ? numeric_limits::lowest()\n : static_cast(rhs)\n : static_cast(rhs);\n }\n namespace _overflow_impl {\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs+rhs)\n {\n return lhs+rhs;\n }\n };\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs+rhs)\n {\n using result_type = decltype(lhs+rhs);\n using numeric_limits = numeric_limits;\n return _overflow_impl::return_if(\n !((rhs>=from_rep{}(0))\n ? (lhs>numeric_limits::max()-rhs)\n : (lhs\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> _impl::op_result<_impl::add_op, Lhs, Rhs>\n {\n using result_type = decltype(lhs+rhs);\n using numeric_limits = numeric_limits;\n return (rhs>0)\n ? (lhs>numeric_limits::max()-rhs) ? numeric_limits::max() : lhs+rhs\n : (lhs\n constexpr auto add(OverflowTag, Lhs const& lhs, Rhs const& rhs)\n -> decltype(lhs+rhs)\n {\n return _impl::for_rep(_overflow_impl::binary_operator(), lhs, rhs);\n }\n namespace _overflow_impl {\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs-rhs)\n {\n return lhs-rhs;\n }\n };\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs-rhs)\n {\n using result_type = decltype(lhs-rhs);\n using numeric_limits = numeric_limits;\n return _overflow_impl::return_if(\n (rhs{}(0))\n ? (lhs<=numeric_limits::max()+rhs)\n : (lhs>=numeric_limits::lowest()+rhs),\n lhs-rhs,\n \"positive overflow in subtraction\");\n }\n };\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> _impl::op_result<_impl::subtract_op, Lhs, Rhs>\n {\n using result_type = decltype(lhs-rhs);\n using numeric_limits = numeric_limits;\n return (rhs<0)\n ? (lhs>numeric_limits::max()+rhs) ? numeric_limits::max() : lhs-rhs\n : (lhs\n constexpr auto subtract(OverflowTag, Lhs const& lhs, Rhs const& rhs)\n -> decltype(lhs-rhs)\n {\n return _impl::for_rep(_overflow_impl::binary_operator(), lhs, rhs);\n }\n namespace _overflow_impl {\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs*rhs)\n {\n return lhs*rhs;\n }\n };\n template\n constexpr bool is_multiply_overflow(Operand const& lhs, Operand const& rhs)\n {\n using result_nl = numeric_limits;\n return lhs && rhs && ((lhs>Operand{0})\n ? ((rhs>Operand{0}) ? (result_nl::max()/rhs) : (result_nl::lowest()/rhs))Operand{0}) ? (result_nl::lowest()/rhs) : (result_nl::max()/rhs))>lhs);\n }\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs*rhs)\n {\n return _overflow_impl::return_if(\n !is_multiply_overflow(lhs, rhs),\n lhs*rhs, \"overflow in multiplication\");\n }\n };\n template<>\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> _impl::op_result<_impl::multiply_op, Lhs, Rhs>\n {\n using result_type = decltype(lhs*rhs);\n return is_multiply_overflow(lhs, rhs)\n ? ((lhs>0) ^ (rhs>0))\n ? numeric_limits::lowest()\n : numeric_limits::max()\n : lhs*rhs;\n }\n };\n }\n template\n constexpr auto multiply(OverflowTag, Lhs const& lhs, Rhs const& rhs)\n -> decltype(lhs*rhs)\n {\n return _impl::for_rep(_overflow_impl::binary_operator(), lhs, rhs);\n }\n namespace _overflow_impl {\n template\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs/rhs)\n {\n return lhs/rhs;\n }\n };\n }\n namespace _overflow_impl {\n template\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs>>rhs)\n {\n return lhs>>rhs;\n }\n };\n }\n namespace _overflow_impl {\n template\n constexpr bool is_shift_left_overflow(Lhs const& lhs, Rhs const& rhs)\n {\n using result_type = decltype(lhs<0 && unsigned(cnl::leading_bits(static_cast(lhs)))\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs<\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> decltype(lhs<\n struct binary_operator {\n template\n constexpr auto operator()(Lhs const& lhs, Rhs const& rhs) const\n -> _impl::op_result<_impl::shift_left_op, Lhs, Rhs>\n {\n using result_type = decltype(lhs<0) ^ (rhs>0))\n ? numeric_limits::lowest()\n : numeric_limits::max()\n : lhs<\n constexpr auto shift_left(OverflowTag, Lhs const& lhs, Rhs const& rhs)\n -> decltype(lhs<(_overflow_impl::binary_operator(), lhs, rhs);\n }\n}\nnamespace cnl {\n template\n class overflow_integer;\n namespace _integer_impl {\n template\n struct is_overflow_integer\n : std::false_type {\n };\n template\n struct is_overflow_integer>\n : std::true_type {\n };\n template\n struct common_type;\n template\n struct common_type<\n overflow_integer,\n overflow_integer> {\n using type = overflow_integer<\n typename std::common_type::type,\n OverflowTag>;\n };\n template\n struct common_type<\n overflow_integer, RhsInteger,\n _impl::enable_if_t<\n !_integer_impl::is_overflow_integer::value && std::is_integral::value>> {\n using type = typename cnl::overflow_integer::type, LhsOverflowTag>;\n };\n template\n struct common_type<\n overflow_integer, Float,\n _impl::enable_if_t::value>> {\n using type = typename std::common_type::type;\n };\n template\n struct common_type>\n : common_type, Lhs> {\n };\n }\n template\n class overflow_integer : public _impl::number_base, Rep> {\n static_assert(!_integer_impl::is_overflow_integer::value,\n \"overflow_integer of overflow_integer is not a supported\");\n public:\n using rep = Rep;\n using overflow_tag = OverflowTag;\n using _base = _impl::number_base, Rep>;\n constexpr overflow_integer() = delete;\n template\n constexpr overflow_integer(overflow_integer const& rhs)\n :overflow_integer(to_rep(rhs))\n {\n }\n template::value, int> dummy = 0>\n constexpr overflow_integer(Rhs const& rhs)\n :_base(convert(overflow_tag{}, rhs))\n {\n }\n template< ::cnl::intmax Value>\n constexpr overflow_integer(constant)\n : _base(static_cast(Value))\n {\n static_assert(Value <= numeric_limits::max(), \"initialization by out-of-range value\");\n static_assert(!numeric_limits::is_signed || Value >= numeric_limits::lowest(), \"initialization by out-of-range value\");\n }\n template\n constexpr explicit operator T() const\n {\n return static_cast(to_rep(*this));\n }\n };\n namespace _impl {\n template\n struct get_rep> {\n using type = Rep;\n };\n template\n struct set_rep, NewRep> {\n using type = overflow_integer;\n };\n }\n template\n struct digits> : digits {\n };\n template\n struct set_digits, MinNumBits> {\n using type = overflow_integer, OverflowTag>;\n };\n template\n constexpr Rep to_rep(overflow_integer const& number)\n {\n using base_type = typename overflow_integer::_base;\n return to_rep(static_cast(number));\n }\n template\n struct from_rep> {\n template\n constexpr auto operator()(Rep const& r) const\n -> overflow_integer\n {\n return r;\n }\n };\n template\n struct from_value, Value> {\n using type = overflow_integer;\n };\n template\n struct from_value, overflow_integer> {\n private:\n using _overflow_tag = _impl::common_type_t;\n using _rep = from_value_t;\n public:\n using type = overflow_integer<_rep, _overflow_tag>;\n };\n template\n struct from_value, constant> {\n using _rep = typename std::conditional::value::type;\n using type = overflow_integer<_rep, OverflowTag>;\n };\n template\n struct shift>\n : shift, Rep>> {\n };\n template\n constexpr auto make_overflow_int(Rep const& value)\n -> overflow_integer\n {\n return value;\n }\n namespace _impl {\n template\n struct unary_operator> {\n constexpr auto operator()(overflow_integer const& operand) const\n -> decltype(overflow_integer(Operator()(to_rep(operand))))\n {\n return overflow_integer(Operator()(to_rep(operand)));\n }\n };\n template\n struct binary_operator, overflow_integer,\n typename Operator::is_not_comparison> {\n constexpr auto operator()(\n overflow_integer const& lhs,\n overflow_integer const& rhs) const\n -> decltype(make_overflow_int(_overflow_impl::binary_operator()(to_rep(lhs), to_rep(rhs))))\n {\n return make_overflow_int(\n _overflow_impl::binary_operator()(to_rep(lhs), to_rep(rhs)));\n }\n };\n template\n struct binary_operator, overflow_integer,\n typename Operator::is_not_comparison> {\n constexpr auto operator()(\n overflow_integer const& lhs,\n overflow_integer const& rhs) const\n -> overflow_integer(), std::declval())), OverflowTag>\n {\n using result_rep_type = decltype(Operator{}(std::declval(), std::declval()));\n using result_type = overflow_integer;\n return _impl::from_value(binary_operator{}(lhs, rhs));\n }\n };\n template\n struct binary_operator, overflow_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n overflow_integer const& lhs,\n overflow_integer const& rhs) const\n -> decltype(Operator()(to_rep(lhs), to_rep(rhs)))\n {\n return Operator()(to_rep(lhs), to_rep(rhs));\n }\n };\n template\n struct binary_operator, overflow_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n const overflow_integer& lhs,\n const overflow_integer& rhs) const\n -> decltype(binary_operator<\n Operator,\n overflow_integer, cnl::_impl::common_type_t>,\n overflow_integer, cnl::_impl::common_type_t>>()(lhs, rhs))\n {\n using common_rep = cnl::_impl::common_type_t;\n using common_tag = cnl::_impl::common_type_t;\n return binary_operator<\n Operator,\n overflow_integer,\n overflow_integer>()(lhs, rhs);\n }\n };\n }\n}\nnamespace cnl {\n template\n struct numeric_limits>\n : numeric_limits, Rep>> {\n static constexpr bool is_integer = true;\n };\n template\n struct numeric_limits const>\n : numeric_limits, Rep>> {\n static constexpr bool is_integer = true;\n };\n}\nnamespace std {\n template<\n class Lhs,\n class RhsRep, class RhsOverflowTag>\n struct common_type<\n Lhs,\n cnl::overflow_integer>\n : cnl::_integer_impl::common_type<\n Lhs,\n cnl::overflow_integer> {\n };\n template<\n class LhsRep, class LhsOverflowTag,\n class Rhs>\n struct common_type<\n cnl::overflow_integer,\n Rhs>\n : cnl::_integer_impl::common_type<\n cnl::overflow_integer,\n Rhs> {\n };\n template<\n class LhsRep, class LhsOverflowTag,\n class RhsRep, int RhsExponent>\n struct common_type<\n cnl::overflow_integer,\n cnl::fixed_point>\n : std::common_type<\n cnl::fixed_point, 0>,\n cnl::fixed_point> {\n };\n template<\n class LhsRep, int LhsExponent,\n class RhsRep, class RhsOverflowTag>\n struct common_type<\n cnl::fixed_point,\n cnl::overflow_integer>\n : std::common_type<\n cnl::fixed_point,\n cnl::fixed_point, 0>> {\n };\n template<\n class LhsRep, class LhsOverflowTag,\n class RhsRep, class RhsOverflowTag>\n struct common_type<\n cnl::overflow_integer,\n cnl::overflow_integer>\n : cnl::_integer_impl::common_type<\n cnl::overflow_integer,\n cnl::overflow_integer> {\n };\n template\n struct numeric_limits>\n : cnl::numeric_limits> {\n };\n template\n struct numeric_limits const>\n : cnl::numeric_limits> {\n };\n}\nnamespace cnl {\n struct closest_rounding_tag {\n template\n static constexpr To convert(From const& from)\n {\n return static_cast(intmax(from+((from>=0) ? .5 : -.5)));\n }\n };\n template\n class rounding_integer;\n namespace _rounding_integer_impl {\n template\n struct is_rounding_integer : std::false_type {\n };\n template\n struct is_rounding_integer> : std::true_type {\n };\n }\n template\n class rounding_integer : public _impl::number_base, Rep> {\n static_assert(!_rounding_integer_impl::is_rounding_integer::value,\n \"rounding_integer of rounding_integer is not a supported\");\n using super = _impl::number_base, Rep>;\n public:\n using rounding = RoundingTag;\n using _base = _impl::number_base, Rep>;\n constexpr rounding_integer() = default;\n template::is_integer, int> Dummy = 0>\n constexpr rounding_integer(T const& v)\n : super(static_cast(v)) { }\n template::is_integer, int> Dummy = 0>\n constexpr rounding_integer(T const& v)\n : super(rounding::template convert(v)) { }\n template\n constexpr explicit operator T() const\n {\n return static_cast(to_rep(*this));\n }\n };\n template\n struct digits> : digits {\n };\n template\n struct set_digits, MinNumBits> {\n using type = rounding_integer, RoundingTag>;\n };\n template\n struct from_rep> {\n template\n constexpr auto operator()(Rep const& r) const\n -> rounding_integer\n {\n return r;\n }\n };\n template\n constexpr Rep to_rep(rounding_integer const& number)\n {\n using base_type = typename rounding_integer::_base;\n return to_rep(static_cast(number));\n }\n namespace _impl {\n template\n struct get_rep> {\n using type = Rep;\n };\n template\n struct set_rep, NewRep> {\n using type = rounding_integer;\n };\n }\n template\n struct from_value, Value> {\n using type = rounding_integer;\n };\n template\n struct from_value, rounding_integer> {\n private:\n using _overflow_tag = _impl::common_type_t;\n using _rep = from_value_t;\n public:\n using type = rounding_integer<_rep, _overflow_tag>;\n };\n template\n struct from_value, constant> {\n using _rep = typename std::conditional::value::type;\n using type = rounding_integer<_rep, RoundingTag>;\n };\n template\n struct shift>\n : shift, Rep>> {\n };\n namespace _impl {\n template\n struct unary_operator> {\n constexpr auto operator()(rounding_integer const& operand) const\n -> decltype(from_rep>{}(\n Operator()(to_rep(operand))))\n {\n using result_type = rounding_integer;\n return from_rep{}(Operator()(to_rep(operand)));\n }\n };\n }\n namespace _impl {\n template\n struct binary_operator, rounding_integer,\n typename Operator::is_not_comparison> {\n constexpr auto operator()(\n rounding_integer const& lhs,\n rounding_integer const& rhs) const\n -> decltype(from_rep, RoundingTag>>{}(\n Operator()(to_rep(lhs), to_rep(rhs))))\n {\n using result_type = rounding_integer, RoundingTag>;\n return from_rep{}(Operator()(to_rep(lhs), to_rep(rhs)));\n }\n };\n template\n struct binary_operator, rounding_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n rounding_integer const& lhs,\n rounding_integer const& rhs) const\n -> decltype(Operator()(to_rep(lhs), to_rep(rhs)))\n {\n return Operator()(to_rep(lhs), to_rep(rhs));\n }\n };\n template\n struct binary_operator, rounding_integer,\n typename Operator::is_comparison> {\n constexpr auto operator()(\n rounding_integer const& lhs,\n rounding_integer const& rhs) const\n -> decltype(binary_operator>, rounding_integer>>()(lhs, rhs))\n {\n using common_tag = common_type_t;\n return binary_operator, rounding_integer>()(lhs, rhs);\n }\n };\n }\n template\n constexpr auto operator<<(\n rounding_integer const& lhs,\n RhsInteger const& rhs)\n -> decltype(from_rep>{}(to_rep(lhs) << rhs))\n {\n return from_rep>{}(to_rep(lhs) << rhs);\n }\n template\n struct numeric_limits>\n : numeric_limits, Rep>> {\n static constexpr bool is_integer = true;\n };\n template\n struct numeric_limits const>\n : numeric_limits, Rep>> {\n static constexpr bool is_integer = true;\n };\n}\nnamespace std {\n template\n struct numeric_limits>\n : cnl::numeric_limits> {\n };\n template\n struct numeric_limits const>\n : cnl::numeric_limits> {\n };\n}\n\n#endif // CNL_COMPLETE_H\n","stdin","compiler","warning,boost-1.66.0-gcc-head,gnu++2a,cpp-no-pedantic","createdAt",1524363265,"title","description","isPrivate","compilerInfo",{"_11":59,"_13":59,"_15":59,"_17":59,"_19":3402,"_22":25,"_24":25,"_26":59,"_28":3403},[],[],"results",[3406,3410,3413,3416],{"_31":3407,"_3408":3409},"Control","data","Start",{"_31":3411,"_3408":3412},"StdOut","n=8\ndigits=15\ninteger range=[1..32767]\nscale=1/256 = 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C++.","",{"_3429":3505,"_3431":3506},"2.3.0","2024-06-15T20:23:18Z",{"_3429":3505,"_3431":3506},{"_11":3509,"_3422":3510,"_3398":3511,"_3425":3512,"_3427":3513,"_3433":3516},"rapidcsv","d99kris/rapidcsv","C++ CSV parser library","",{"_3429":3514,"_3431":3515},"v8.85","2025-03-22T01:58:55Z",{"_3429":3517,"_3431":3518},"v8.84","2024-09-28T05:31:16Z",{"_11":3520,"_3422":3521,"_3398":3522,"_3425":3523,"_3427":3524,"_3433":3527},"fmt","fmtlib/fmt","A modern formatting library","",{"_3429":3525,"_3431":3526},"11.2.0","2025-05-03T16:40:00Z",{"_3429":3528,"_3431":3529},"11.1.4","2025-02-26T18:33:33Z",{"_11":3531,"_3422":3532,"_3398":3533,"_3425":3534,"_3427":3535,"_3433":3538},"NumCpp","dpilger26/NumCpp","C++ implementation of the Python Numpy 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